My PC wants to be a weird Gun Chemist/Barbarian thing, story reason wont get into here.
My question is, can a raging barbarian infuse a gun with the alchemist infuse ability?
Alchemists in general & gun chemists in particular don't get an infuse ability. What do you mean?
Sorry, his Alchemical Ordnance I think. He calls it "infusion."
When he adds fire, or entangle or ice to his shots.
Alchemical ordnance is a supernatural ability & has no concentration check or skill check associated. Your character is probably OK to use it during a rage.